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Thermomechanical loading applied on the cladding tubeduring the pellet cladding mechanical interaction phase

of a rapid reactivity initiated accidentArthur Hellouin de Menibus, Jérôme Sercombe, Quentin Auzoux, Christophe

Poussard

To cite this version:Arthur Hellouin de Menibus, Jérôme Sercombe, Quentin Auzoux, Christophe Poussard. Thermome-chanical loading applied on the cladding tube during the pellet cladding mechanical interaction phaseof a rapid reactivity initiated accident. Journal of Nuclear Materials, Elsevier, 2014, 453, pp.210-213.�10.1016/j.jnucmat.2014.06.046�. �hal-01057281�

Thermomechanical Loading Applied on the

Cladding Tube During the Pellet Cladding

Mechanical Interaction Phase of a Rapid

Reactivity Initiated Accident

Arthur Hellouin de Menibus∗1, Jerome Sercombe2, QuentinAuzoux3, and Christophe Poussard3

1CEA Saclay/DEN/DANS/DMN/SRMA, 91191 Gif-sur-Yvette, France2CEA Cadarache/DEN/CAD/DEC/SESC, 13108 St Paul lez Durance, France

3CEA Saclay/DEN/DANS/DMN/SEMI, 91191 Gif-sur-Yvette, France

Published in 2014 in the Journal of Nuclear MaterialsVolume 453, Issues 13, October 2014, Pages 210 to 213

http://www.sciencedirect.com/science/article/pii/S0022311514004036

Abstract

Calculations of the CABRI REP-Na5 pulse were performed withthe ALCYONE code in order to determine the evolution of the ther-momechanical loading applied on the cladding tube during the Pellet-Cladding Mechanical Interaction (PCMI) phase of a rapid ReactivityInitiated Accident (RIA) initiated at 280 ◦C that lasted 8.8ms. Theevolution of the following parameters are reported : the cladding tem-perature, heating rate, strain rate and loading biaxiality. The impactof these parameters on the cladding mechanical behavior and fractureare then briefly reviewed.

Keywords : Zirconium, Cladding Tube, Reactivity Initiated Accident (RIA)

∗Tel.: +33 1 69 08 39 43; e-mail: arthur.hellouin-de-menibus@cea.fr

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1 Introduction

The most critical postulated RIA scenario in a nuclear pressurized water re-actor is a control rod ejection (REA : Rod Ejection Accident) that inducesa large energy deposition in the surrounding fuel pellets [1]. As a conse-quence, the pellets from the surrounding fuel rods expand suddenly, whichinduces deformation and heating of the cladding tubes. The approach fol-lowed internationally to study the cladding tubes resistance to fracture inRIA conditions, to in fine improve the accuracy of the associated safetycriteria, is divided into three complementary parts:

1. Integral tests performed on one instrumented fuel rod at a time innuclear research reactors;

2. Dedicated multi-physical codes, which model the pellet and/or claddingtube behaviour during the RIA transient. These codes allowed for in-stance to identify the thermomechanical loading applied on the claddingtube;

3. In-laboratory tests and associated numerical simulations to study sep-arately, or in a partially coupled way, the effect of different parameterson the pellet and cladding tube behaviour. Focusing on the mechani-cal behaviour of cladding tubes, such parameters are for instance thetemperature level, the strain rate, the stress state, the characteristicsof the contact between pellet and cladding tube and the loading mode(displacement or load controlled), the irradiation level, the hydrogenand hydrides concentration and distribution, etc.

The RIA chronological scenario were described in numerous reports [1, 2].The generally reported thermomechanical loading for the Pellet CladdingMechanical Interaction (PCMI) phase are the following. The strain rate ison the order of 1/s [1]. The cladding temperature depends on the pulsecharacteristics, but it typically reaches 600 - 800 ◦C at fracture on the innerside and about 300 ◦C on the outer side when the initial coolant temperatureis 286 ◦C [3]. The cladding tube heating rate is about 104 K/s [1]. The loadingtriaxiality level is included between plane-strain (εzz = 0) and equibiaxial(εθθ = εzz) conditions [4]. Nevertheless, data on the evolution of the loadingapplied on the cladding tube during the PCMI phase starting from PWRworking temperature are scarce in the open litterature.

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Thus, CABRI REP-Na5 calculations with the ALCYONE code developedat the CEA [5, 6] were performed in the present study to evaluate the evo-lution of the thermomechanical loading during the PCMI phase. A materialanisotropic plastic behaviour law for the cladding tube that was specificallyidentified in RIA-PCMI conditions by Le Saux et al. [7] was used.

First ALCYONE code and procedures are described, together with theCABRI REP-Na5 characteristics. Then, the evolution of the thermomechan-ical loading on the cladding is exposed in terms of temperature, heating rate,strain rate and loading biaxiality and are compared with the generally re-ported range for these parameters. The impact of these parameters on thecladding mechanical behavior and fracture are then reviewed.

2 ALCYONE code and procedures

ALCYONE is a multi-dimensional code used to study the behaviour of PWRfuel rods during normal, off-normal and accidental conditions [5, 6]. ALCY-ONE output results from the 1.5D fuel rod scheme for the CABRI REP-Na5pulse [8] were used in the present study to determine the evolution of thethermomechanical loading on the cladding tube in RIA PCMI phase. Thisintegral test was done on a 64 GWd/tU irradiated Zircaloy-4-UO2 rod witha maximum oxide thickness of 25µm . The peak mid-height width was 8.8ms and the enthalpy was 104 cal/g. The tests were performed in a sodiumcoolant at an initial temperature of 280 ◦C. ALCYONE calculations of theREP-Na tests led to results in very good agreement with the measured post-test axial profilometry, clad and fuel elongations [5] (figure 1(a) shows thecalculated and measured clad diameter before and after the REP-Na5 pulsetest). Since this first publication of this work, the modelling of the heat andmass transport in the sodium coolant has been improved by a description ofthe heat exchanges between the coolant and the outer Niobium ring of theCABRI experimental rig. The instrumentation device of the REP-Na testsincluded thermocouples placed at several axial and azimuthal locations whichwere be used to assess the quality of the heat radial and axial transfer in thefuel pellet - cladding - coolant system. The coolant variations of temperatureduring the REP-Na5 are extremely well reproduced by ALCYONE (figure1(b)) with the assumption of a very high conductance at the pellet-clad in-terface. This assumption already stressed in SCANAIR calculations of theREP-Na tests [9] is of great importance with respect to the evaluation of the

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thermal gradient in the cladding. In ALCYONE 1.5D model, the REP-Na5refabricated rod is simulated with 10 axial slices of equal height. All theresults presented in the next parts are relative to the slice situated at themaximum Linear Heat Rate (LHR).

3 Results and analysis : thermomechanical

loading on the cladding tube during the

PCMI phase

3.1 Temperature

In a time interval right after the pulse maximum where various rod fracturewere observed [3], the cladding inner surface temperature is between 700 ◦Cand 800 ◦C. At this time, it is about 300 ◦C on the outer surface (figure 2(a)).These temperatures are similar to the ones calculated with the RANNS codefor the Va-3 pulse in NSRR (4.4 ms and 82 cal/g peak - Sugiyama et al. [3]).The results of Sugiyama et al. [3] showed that for the same peak enthalpy,a 3 times longer peak does not affect much the minimum and maximumtemperatures. Neverthless, it induced a smoother temperature distribution inthe cladding thickness for longer pulses. The thermal gradient in the claddingtube thickness reduces the tensile circumferential stress on the inner diameterand increases the one on the outer diameter. In addition, as the elasticitymodulus and the yield stress decrease when the temperature increases, thestress levels for a given strain are smaller on the inner diameter than on theouter one. Both effects induce higher stress levels on the outer surface thanon the inner one (figure 2(b)). Sugiyama et al. [3] results indicated that 60%and 85% of the cladding section was at a temperature lower than 350 ◦C and480 ◦C respectively at cladding fracture. In laboratory tests that aimed atstudying RIA conditions should therefore take into account the temperaturelevel as it affects the material mechanical and thermal behaviour [7] andthe fracture process [10, 11, 12], the quantity of dissolved hydrides [13] andthe extent of the irradiation recovery [14]. The temperature gradient in thecladding wall is likely one of the thermomechanical loading conditions that ismost difficult to reproduce experimentally. This aspect may nevertheless beadressed by computational analyses, such as those of the present study, byusing a material behaviour law identified in isothermal conditions covering

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(a)

260

280

300

320

340

360

380

400

420

0 2 4 6 8 10

Na tem

pera

ture

(C

)

Time (s)

Exp.Alcyone

(b)

Figure 1: Calculated and measured clad diameters and sodium temperaturesfor the CABRI REP-Na5 pulse: (a) clad diameter before and after the pulseand (b) sodium temperature during the pulse at the position of the maximumLinear Heat Rate.

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the PCMI phase representative temperature range.

(a)

(b)

Figure 2: ALCYONE outputs for the CABRI REP-Na5 pulse: (a) claddingtemperature and (b) stress levels.

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3.1.1 Heating rate

The maximum heating rate calculated by ALCYONE is 104 ◦C/s on the outersurface, in good agreement with NEA [1] data, but is 5 times higher on theinner surface (figure 3(a)). To the authors knowledge, no work is availableon the irradiation recovery or the dislocation recovery and the material re-crystallisation at such high heating rate. Recent results obtained at 350 ◦Cand high heating rate (about 2-5×103 ◦C/s) indicated that the hydride dis-solution might be fast enough so that the high heating rate, measured byinfrared pyrometry techniques, does not affect the hydrogen partition intohydrogen and hydrides at a given temperature [15]. This result is in contra-diction with Kearns [13] results. He estimated the complete dissolution of100-200ppm hydrided samples at 350 ◦C was higher than 10 seconds, whichis 100 times longer than the experiments carried out in [15]. The resultsreported by Yueh et al. [15] might be explained by the limited influence of100-130ppm of hydrides at 350 ◦C [10] ( 100ppm is the quantity dissolved at350 ◦C at low heating rates).

3.2 Circumferential strain rate

The circumferential strain rate calculated by ALCYONE is between 0.9/s and1.3/s (figure 3(b)). This is in agreement with the 1/s strain rate indicatedby the NEA [1]. Longer pulses leads to lower circumferential strain rates,for example 0.15/s in the 76ms mid-width duration REP-Na4 pulse [1]. It isimportant to consider RIA representative strain rates in experiments aimingat studying the cladding fracture in the PCMI phase. Indeed, it was shownthat strain rates higher than 0.1/s can induce material heating due to plasticdissipation [16]. More precisely, average temperature increases (10-15 ◦C)were measured in the range 0.1 - 1/s, but not strongly localized due totemperature homogenization by thermal conduction, while high and stronglylocalized temperature increases (more than 100 ◦C) were measured in therange 1-10/s [16]. Local heating could enhance strain localization, whichitself would reinforce the temperature localization and so on.

3.3 Loading biaxiality

The mechanical loading is mainly due to fuel pellet expansion, which inducea ratio of the plastic axial strain divided by the plastic circumferential strain

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(a)

(b)

Figure 3: ALCYONE outputs for the CABRI REP-Na5 pulse: (a) heatingrate and (b) circumferential strain rate.

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εpzz/εp

θθ between 0.2 and 0.7 in CABRI REP Na tests based on postmortemmeasurements (Cazalis et al. [4]). The associated ratio of the axial stress onthe circumferential stress σzz/σθθ depends on the material anisotropy. Theequivalent stress (σeq) using the Hill plasticity criterion and neglecting theshear terms is :

σ2

eq = Hrr(σθθ − σzz)2 +Hθθ(σzz − σrr)

2 +Hzz(σrr − σθθ)2 (1)

Using this potential for the material constitutive equation :

ε̇p = λ̇∂σeq

∂σ̄(2)

it results in :

εpzzεpθθ

=(Hrr +Hθθ)

σzz

σθθ

−Hrr

Hrr +Hzz −Hrr

σzz

σθθ

(3)

The CWSR Zircaloy-4 anisotropy coefficients were identified in the me-chanical behaviour model developed by Le Saux et al. [7] :

Hrr = 0, 485 +0, 095× (1− Φ)

1 + exp(12(T/740− 1))+

0.32Φ

1 + exp(10(T/660− 1))

Hθθ = 1−Hrr

Hzz = 0, 52 +(4× 10−4

− 0, 23)(1− Φ)

1 + exp(15(T/550− 1))−

0.16Φ

1 + exp(20(T/920− 1))

(4)

with T the temperature in kelvin and Φ is a neutron fluence (φ) dependentvariable, in 1025n/m2 :

Φ = (1− 0.3φ) (5)

Thus, the relationship between the strain and stress ratio depends onboth the temperature and the irradiation level (figure 4(a)). In the REP-Na5 pulse, ALCYONE estimates that the stress ratio is between 0.6 and 0.95(figure 4(b)), in agreement with the measured and theoretically predictedvalues (figure 4(a)). Representative loading biaxialities should be taken intoaccount as the detrimental effect of a high biaxiality level mechanical loadingon the ductile fracture is well known [17]. Concerning zirconium alloys, thiseffect was confirmed on unirradiated recrystallized Zircaloy-2 sheets [18], onunirradiated recrystallized Zircaloy-2 tubes [19], on unirradiated recrystal-lized Zircaloy-4 [20], on unirradiated and irradiated Zr-1%Nb tubes [21] andon unirradiated CWSR Zircaloy-4 by means of EDC and HB-EDC tests [22].

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(a)

(b)

Figure 4: Figure (a) represents the strain biaxiality ratio obtained from exter-nal diameter and total rod axial elongation measurements after integral testsversus the stress biaxiality ratio, which depends on the material anisotropy.Figure (b) represents the stress biaxiality ratio estimated by ALCYONE forCABRI REP-Na5.

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4 Conclusion

ALCYONE calculations of CABRI REP-Na5 pulse were performed to eval-uate the evolution of the thermo-mechanical loading on the cladding tubeduring the whole transient of a rapid RIA transient (8.8ms pulse width).The results can be summarized as follow :

• The temperature rise quickly up to 700-800 ◦C on the inner diameter,while it remains about 300 ◦C on the external diameter. This tempera-ture range is covered by some already published material data and con-stitutive equations [7] and the thermal gradient aspect is taken into ac-count in numerical simulations such as the one described in the presentpaper.

• The heating rate is about 104 ◦C/s on the outer diameter but is about5 times higher on the inner diameter. Additional work is required toquantify the impact on the evolution of the material microstructureand properties of such a high strain rate.

• The circumferential strain rate is between 0.9 and 1.3/s. Additionalwork is required to evaluate the impact of the local heating due toplastic dissipation on the material fracture in this intermediate strainrate range where adiabatic assumption are not valid [16].

• The stress biaxiality is between 0.6 and 0.95. Efforts are currentlyunderway to develop easy-to-use testing techniques on cladding tubesthat cover such loading biaxiality levels [22, 12, 23].

5 Bibliography

References

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[2] T. Fuketa, T. Sugiyama, Current RIA-related regulatory criteria inJapan and their technical basis, in: Workshop RIA, Paris, France, 2009.

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